Lecture 05: Aperture Photometry

ASTR 210 Observational Astronomy and Data Reduction

Context and Why This Matters

Aperture photometry converts pixel counts into a calibrated brightness, but the same star can yield different reported magnitudes depending on aperture radius, sky-annulus placement, and how carefully the zero point was derived. Photometry is a measurement-design problem, not only an arithmetic one.

Learning Goals

  1. Define instrumental magnitude and photometric zero point.
  2. Derive a zero point from one standard star and verify it against two others.
  3. Explain how aperture and sky-annulus choice bias a photometric measurement.

Opening Phenomenon

A photometric pipeline processes three standard stars in the same field and filter. If the zero point derived from one star is correct, it should reproduce the catalog magnitudes of the other two without further adjustment.

Terms Developed in Context

These terms form the measurement chain for Aperture Photometry: each connects an observable to a model choice, and each has a boundary that must be respected when making a scientific claim.

instrumental magnitude

A logarithmic measure computed directly from a background-subtracted detector count rate before absolute calibration. It places measured flux on a convenient relative scale that can be tied to catalog standards.

The usual definition is \(m_{inst}=-2.5\log_{10}(C/t)\), and the calibrated magnitude adds a zero point and any needed color/extinction terms. Instrumental magnitudes from different systems or nights are not directly comparable without calibration.

Developed in this lecture: The term helps interpret this evidence: STD-A: 150000 counts in a 30 s exposure, catalog V = 10.21. It also constrains the working model: Instrumental magnitude is defined from a count rate (counts per second), not raw counts, so exposures of different length can be compared.

zero point

The additive constant that maps an instrumental magnitude scale onto a specified standard magnitude system. It converts count rates into calibrated magnitudes and carries calibration uncertainty into every target result.

For a standard, \(ZP=m_{cat}+2.5\log_{10}(C/t)\); independent standards test whether the value is stable. A zero point can depend on filter, atmosphere, detector, and time; it is not a permanent property of the telescope.

Developed in this lecture: The term helps interpret this evidence: STD-A: 150000 counts in a 30 s exposure, catalog V = 10.21. It also constrains the working model: Instrumental magnitude is defined from a count rate (counts per second), not raw counts, so exposures of different length can be compared.

aperture radius

The distance from a source center defining which pixels are included in circular-aperture photometry. It controls how much of the point-spread function is captured and how much background noise enters.

A curve of growth plots enclosed counts against radius and helps identify a radius where added source flux becomes small. A radius chosen for one seeing condition or crowded field may be inappropriate for another.

Developed in this lecture: The term helps interpret this evidence: STD-A: 150000 counts in a 30 s exposure, catalog V = 10.21. It also constrains the working model: Instrumental magnitude is defined from a count rate (counts per second), not raw counts, so exposures of different length can be compared.

sky annulus

A ring around the source aperture used to estimate the local background level per pixel. It provides the background subtraction needed to isolate source counts from sky and detector background.

Net counts are \(C_{ap}-n_{ap}\bar C_{sky}\), so annulus contamination directly biases the measured flux. The annulus must avoid source wings, neighboring stars, gradients, and bad pixels; “nearby” does not guarantee representative sky.

Developed in this lecture: The term helps interpret this evidence: STD-A: 150000 counts in a 30 s exposure, catalog V = 10.21. It also constrains the working model: Instrumental magnitude is defined from a count rate (counts per second), not raw counts, so exposures of different length can be compared.

count rate

Background-subtracted detector counts divided by exposure time. It permits photometric comparison among frames with different exposure durations.

Magnitude calibration uses \(C/t\) inside the logarithm rather than total counts alone. Count rate corrects exposure duration, not changes in transparency, airmass, or detector response.

Developed in this lecture: The term helps interpret this evidence: STD-A: 150000 counts in a 30 s exposure, catalog V = 10.21. It also constrains the working model: Instrumental magnitude is defined from a count rate (counts per second), not raw counts, so exposures of different length can be compared.

photometric standard

A star with a well-characterized magnitude in a defined passband, observed to calibrate an instrumental system. Standards anchor the zero point and reveal whether the night and reduction are photometrically consistent.

Catalog magnitude and measured count rate determine the zero point; additional standards test color and extinction residuals. A bright isolated star is not automatically a standard, and catalog passbands must match the measurement system.

Developed in this lecture: The term helps interpret this evidence: STD-A: 150000 counts in a 30 s exposure, catalog V = 10.21. It also constrains the working model: Instrumental magnitude is defined from a count rate (counts per second), not raw counts, so exposures of different length can be compared.

curve of growth

The cumulative background-subtracted source counts measured as aperture radius increases. It shows where most source flux has been enclosed without adding excessive background noise.

The plateau indicates diminishing additional flux and supports an evidence-based aperture choice. In crowded fields or spatially varying backgrounds, a curve may not plateau cleanly and can include contaminating flux.

Developed in this lecture: The term helps interpret this evidence: STD-A: 150000 counts in a 30 s exposure, catalog V = 10.21. It also constrains the working model: Instrumental magnitude is defined from a count rate (counts per second), not raw counts, so exposures of different length can be compared.

Evidence

Model

Working Equation

\[ m = -2.5\log_{10}(\text{rate}) + {\rm ZP} \]

Worked Example

  1. STD-A count rate = 150000/30 = 5000.0 counts/s.
  2. Solve for the zero point using the catalog magnitude: ZP = 10.21 + 2.5×log10(5000.0) = 10.21 + 9.247 = 19.457.
  3. Apply ZP to STD-B: rate = 2066.7 counts/s, predicted m = −2.5×log10(2066.7) + 19.457 = 11.169 (catalog: 11.17) — agreement to about 1 millimagnitudes.
  4. Apply ZP to STD-C: rate = 800.0 counts/s, predicted m = −2.5×log10(800.0) + 19.457 = 12.200 (catalog: 12.2) — agreement to about 0 millimagnitudes.
  5. Because both independent checks reproduce the catalog values to a few millimagnitudes, this zero point is internally consistent and can be applied to the unknown target in the same field.

Common Misconception

Choosing an aperture radius too small (losing source flux to the wings of the point-spread function) or too large (including excess sky noise), then blaming the resulting magnitude error on "bad seeing" rather than measurement design.

Active-Learning Guidance

Using the STD-A-derived zero point above, predict the magnitude of a fourth star with 38,000 counts in 30 s, then discuss what would make you distrust the prediction.

Lab / Observing Connection

Lab 03 (Aperture Photometry) uses this exact standard-star table to derive and verify a zero point, then applies it to an unknown target.

Synthesis Questions

References